where \(k\in \mathbb {N}\) , \(\textbf {{x}}_k \in \mathbb {R}^n\) , and \(\textnormal {\textbf {u}}_k \in U=\lbrace u_1, \ldots , u_{|U|} \rbrace \)  is a finite set of controls or actions.
\(\textbf {{x}}_k\)  is a discrete-time controlled stochastic process governed by a fully- or partially-unknown, non-linear function \(f:\mathbb {R}^n\times U\rightarrow \mathbb {R}^n \)  driven by an additive noise term \(\textnormal {\textbf {w}}_k \in \mathbb {R}^n\) .
We assume that \(\textnormal {\textbf {w}}_k\)  follows a stationary and independent sub-Gaussian distribution \(p_\textnormal {\textbf {w}}\) .
This includes Gaussian distributions as well as all distributions with bounded support [1]}.
